Episode four of the SpaceTimeMind podcast is now available. This episode features special guest Eric Schwitzgebel. In this first part of our discussion we talk about death, immortality, and logic (and in the second part we talk about consciousness and its relation to biology).
During the first part of the discussion about logic I am pressing the kind of argument that Williamson makes in his new book Modal Logic as Metaphysics (even though none of us have read the book :)). My thought was that since Eric is open to the possibility of Crazyism then he should welcome Williamson’s view as one of the possible crazy options. Eric resists because of a commitment to logical pluralism while Pete resists because modal logic seems disconnected from science and the actual world. At the 87 minute mark I make the crucial move of distinguishing one’s metalogic from first-order logic that would help to answer a lot of Pete’s and Eric’s objections. And of course after we had this discussion I found this paper by Williamson where he makes exactly the same move but with more elegance and sophistication. I am not saying that I endorse Williamson’s view of higher-order modal logic as a science, or that I reject it, but I do think it is an interesting and important position that is worth exploring.
Richard Brown 
This paper / draft of an possible MA thesis of mine just might be relevant to this post / subject 😉 . It’s called “Ways Modality Could be: Revised and Expanded”.
From the introduction:
“In this paper I introduce the idea of a higher-order modal logic—not a modal logic for higher-order predicate logic, but rather a logic of higher-order modalities. “What is a higher-order modality?”, you might be wondering. Well, if a first-order modality is a way that some entity could have been—whether it is a mereological atom, or a mereological complex, or the universe as a whole—a higher-order modality is a way that a first-order modality could have been. First-order modality is modeled in terms of a space of possible worlds—a set of worlds structured by an accessibility relation, i.e., a relation of relative possibility—each world representing a way that the entire universe could have been. A second-order modality would be modeled in terms of a space of spaces of (first-order) possible worlds, each space representing a way that (first-order) possible worlds could have been. And just as there is a unique actual world which represents the way that things actually are, there is a unique actual space which represents the way that first-order modality actually is. One might wonder what the accessibility relation itself is like. Presumably, if it is logical or metaphysical modality that is being dealt with, it is reflexive; but is it also symmetric, or transitive? Especially in the case of metaphysical modality, the answer is not clear. And whichever of these properties it may or may not have, could that itself have been different? Could at least some rival modal logics represent different ways that first-order modality could have been? To be clear, the idea behind my proposal is not just that some things which are possible or necessary might not have been so at the first order, as determined by the actual accessibility relation, but also that the actual accessibility relation, and hence the nature or structure of actual modality, could have been different at some higher order of modality.”
If you’re interested, you can find it here:
http://www.scholardarity.com/?page_id=4022
It’s certainly a crazy-seeming idea, but I think it just might work. 🙂 I’d love to get some of your thoughts if you take a look.
Best,
Jason
BTW, I haven’t had the time to read Williamson’s book or paper yet! Sorry! 😦